Skip to main content
SpringerLink
Log in

The Interplay of Nuclear and Electron Wavepacket Motion in the Control of Molecular Processes: A Theoretical Perspective

  • Chapter
  • First Online:
Molecular Quantum Dynamics

Part of the book series: Physical Chemistry in Action ((PCIA))

Abstract

The concept of coherent control of molecular processes with light is introduced, sketching the way from single parameter to the multiparameter control in the time domain. Optimal control theory is by now a widespread and well-recognized method to solve a variety of control tasks ranging from chemical to physical applications. The underlying concepts and tools with their links to the experiment will be introduced with the focus on chemical reactions. As they include the motion of the nuclei, their time scale ranges from femtoseconds to picoseconds and longer and requires the solution of the time-dependent Schrödinger equation for the nuclear motion. Recent developments that enter the sub-femtosecond domain and open the prospect for direct control of the faster electron motion will be addressed. Two strategies—already realized experimentally—are presented: control of electron dynamics via the carrier envelope phase (CEP) in few-cycle pulses and via the temporal phase of a femtosecond laser pulse with attosecond precision. The issue of nuclear and electronic wavepacket synchronization to achieve control on a chemical reaction is raised. A theoretical method to answer these questions is presented. Finally, a proposal how the electron dynamics can be used as an additional control parameter for a chemical reaction is made.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Messiah A (1962) Quantum mechanics, vol 1. Wiley, New York

    Google Scholar 

  2. Cohen-Tannoudji C, Diu B, Laloe F (1992) Quantum mechanics. Wiley, New York

    Google Scholar 

  3. Basdevant J-L, Dalibard J (2005) Quantum mechanics. Springer, Heidelberg

    Google Scholar 

  4. Tannor DJ (2007) Introduction to Quantum Dynamics: A Time-Dependent Perspective. University Science Books, Sausalito, CA

    Google Scholar 

  5. Pauling L, Wilson EB (1985) Introduction to quantum mechanics with applications to chemistry. Dover Publications, New York

    Google Scholar 

  6. Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43:679

    Google Scholar 

  7. Marcus RA (1993) Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 65:599

    Article  CAS  Google Scholar 

  8. Griebel M, Knapek S, Zumbusch G (2007) Numerical simulation in molecular dynamics. Springer, Heidelberg

    Google Scholar 

  9. Onuhic JN, Wolynes PG (1988) Classical and quantum pictures of reaction dynamics in condensed matter: Resonances, dephasing, and all that. J Phys Chem 92:6495

    Article  Google Scholar 

  10. Herzberg G (1992) Molecular spectra and molecular structure. Krieger, Malabar

    Google Scholar 

  11. Miller WH (2006) Including quantum effects in the dynamics of complex (i.e., large) molecular systems. J Chem Phys 125:132305

    Google Scholar 

  12. Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (2003) Carbon tunneling from a single quantum state. Science 299:867

    Article  CAS  Google Scholar 

  13. McMahon RJ (2003) Chemical reactions involving quantum tunneling. Science 299:833

    Article  CAS  Google Scholar 

  14. Espinosa-García J, Corchado JC, Truhlar DG (1997) The importance of quantum effects for C-H bond activation reactions. J Am Chem Soc 119:9891

    Article  Google Scholar 

  15. Wonchoba SE, Hu W-P, Truhlar DG (1995) Surface diffusion of H on Ni(100). Interpretation of the transition temperature. Phys Rev B 51:9985

    Google Scholar 

  16. Hiraoka K, Sato T, Takayama T (2001) Tunneling reactions in interstellar ices. Science 292:869

    Article  CAS  Google Scholar 

  17. Cha Y, Murray CJ, Klinman JP (1989) Hydrogen tunneling in enzyme-reaction. Science 243:1325

    Article  CAS  Google Scholar 

  18. Kohen A, Cannio R, Bartolucci S, Klinman JP (1999) Enzyme dynamics and hydrogen tunnelling in a thermophilic alcohol dehydrogenase. Nature 399:496

    Article  CAS  Google Scholar 

  19. Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez ML, Villà J (2002) The incorporation of quantum effects in enzyme kinetics modeling. Acc Chem Res 35:341

    Article  CAS  Google Scholar 

  20. Hammer-Schiffer S (2002) Impact of enzyme motion on activity. Biochemistry 41:13335

    Article  Google Scholar 

  21. Antoniou D, Caratzoulas S, Mincer J, Schwartz SD (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions. Eur J Biochem 269:3103

    Article  CAS  Google Scholar 

  22. Ball P (2012) The dawn of quantum biology. Nature 474:272

    Article  Google Scholar 

  23. Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, electronic strucutre, dynamics and spectroscopy. World Scientific, New Jersey

    Google Scholar 

  24. Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, theory, computation and experiment. World Scientific, New Jersey

    Google Scholar 

  25. Worth GA, Cederbaum LS (2001) Mediation of ultrafast electron transfer in biological systems by conical intersections. Chem Phys Lett 338:219–223

    Article  CAS  Google Scholar 

  26. González-Luque M, Garavelli M, Bernardi F, Mechán M, Robb MA, Olivucci M (2010) Computational. Proc Natl Acad Sci USA 97:9379

    Article  Google Scholar 

  27. Polli D, Altoè P, Weingart O, Spillane KM, Manzoni C, Brida D, Tomasello G, Orlandi G, Kukura P, Mathies RA, Garavelli M, Cerullo G (2010) Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467:440

    Article  CAS  Google Scholar 

  28. Engel GS, Calhoun TR, Read EL, Ahn T-K, Mancal T, Cheng Y-C, Blankenship RE, Fleming GR (2007) Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446:782–786

    Article  CAS  Google Scholar 

  29. Lee H, Cheng Y-C, Fleming GR (2007) Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. Science 316:1462

    Article  CAS  Google Scholar 

  30. Collini E, Wong CY, Wilk KE, Curmi PMG, Brumer P, Scholes GD (2010) Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463:644

    Article  CAS  Google Scholar 

  31. Wang Q, Schoenlein RW, Peteanu LA, Shank RA (1994) Vibrationnaly coherent photochemistry in the femtosecond primary event of vision. Science 266:422–424

    Article  CAS  Google Scholar 

  32. Brumer P, Shapiro M (2012) Molecular response in one-photon absorption via natural thermal light vs. pulsed laser excitation. Proc Natl Acad Sci USA 109:19575

    Google Scholar 

  33. Arndt M, Nairz O, Voss-Andreae J, Keller C, van der Zouw G, Zeillinger A (1999) Wave-particle duality of c60 molecules. Nature 401:680

    Article  CAS  Google Scholar 

  34. Gerlich S, Eibenberger S, Tomand M, Nimmrichter S, Hornberger K, Fagan PJ, Tüxen J, Mayor M, Arndt M (2011) Quantum interference of large organic molecules. Nat Phys 2:263

    Google Scholar 

  35. Goulielmakis E, Loh Z-H, Wirth A, Santra R, Rohringer N, Yakovlev VS, Zherebtsov S, Pfeifero T, Azzeer AM, Kling MF, Leone SR, Krausz F (2010) Real-time observation of valence electron motion. Nature 466:739

    Article  CAS  Google Scholar 

  36. Kling MF, Siedschlag C, Verhoef AJ, Khan JI, Schultze M, Uphues T, Ni Y, Uiberacker M, Drescher M, Krausz F, Vrakking MJJ (2006) Control of electron localization in molecular dissociation. Science 312:246

    Article  CAS  Google Scholar 

  37. Niikura H, Légaré F, Hasbani R, Bandrauk AD, Ivanov MY, Villeneuve DM, Corkum PB (2002) Sub-laser-cycle electron pulse for probing molecular dynamics. Nature 417:917

    Article  CAS  Google Scholar 

  38. Stolow A, Jonas DM (2004) Muldimensional snapshots of chemical dynamics. Science 305:1575

    Article  CAS  Google Scholar 

  39. Asssion A, Baumert T, Bergt M, Brixner T, Kiefer B, Seyfried V, Strehle M, Gerber G (1998) Control of chemical reactions by feedback-optimized phase-shaped femtocecond laser pulses. Science 282:919

    Article  Google Scholar 

  40. Brixner T, Damreuer NH, Niklaus P, Gerber G (2001) Photoselective adaptative femtosecond quantum control in the liquid phase. Nature 414:57

    Article  CAS  Google Scholar 

  41. Herek JL, Wohlleben W, Cogdell RJ, Zeidler D, Motzus M (2002) Quantum control of energy flow in light harvesting. Nature 417:533

    Article  CAS  Google Scholar 

  42. Levis RJ, Menkir GM, Rabitz H (2001) Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses. Science 292:709

    Article  CAS  Google Scholar 

  43. Madsen CB, Madsen LB, Viftrup SS, Johansson MP, Poulsen TB, Holmegaard L, Kumarappan V, Jorgensen KA, Stapelfeldt H (2009) Manipulating the torsion of molecules by strong laser pulses. Phys Rev Lett 102:073007

    Article  CAS  Google Scholar 

  44. Holmegaard L, Hansen JL, Kalhøj L, Kragh SL, Stapelfeldt H, Filsinger F, Küpper J, Meijer G, Dimitrovski D, Martiny C, Madsen LB (2010) Photoelectron angular distributions from strong-field ionization of oriented molecules. Nat Phys 6:428

    Article  CAS  Google Scholar 

  45. Bisgaard CZ, Clarkin OJ, Wu G, Lee AMD, Gessner O, Hayden CC, Stolow A (2009) Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules. Science 323:1464

    Article  CAS  Google Scholar 

  46. Bethlem HL, Berden G, Crompvoets FM, Jongma RT, van Roij AJA, Meijer G (2000) Electrostatic trapping of ammonia molecules. Nature 406:491

    Article  CAS  Google Scholar 

  47. Kreckel H, Bruhns H, M, Glover SCO, Miller KA, Urbain X, Savin DW (2010) Experimental results for H2 formation from H− and H and implications for first star formation. Science 329:69

    Google Scholar 

  48. Clary DC (1998) Quantum theory of chemical reaction dynamics. Science 279:1879

    Article  CAS  Google Scholar 

  49. Schnieder L, Seekamp-Rahn K, Borkowski J, Wrede E, Welge KH, Aoiz FJ, Bañares L, D’Mello MJ, Herrero VJ, Rábanos VS, Wyatt RE (1995) Experimental studies and theoretical predictions for the H + D2 → HD + D reaction. Science 269:207

    Article  CAS  Google Scholar 

  50. Qui M, Ren Z, Che L, Dai D, Harich SA, Wang X, Yang X, Xu C, Xie D, Gustafsson M, Skodje RT, Sun Z, Zhang DH (2006) Observation of Feshbach resonances in the F + H2 → HF + H reaction. Science 311:1440

    Article  Google Scholar 

  51. Dong W, Xiao C, Wang T, Dai D, Yang X, Zhang DH (2010) Transition-state spectroscopy of partial wave resonances in the F + HD. Science 327:1501

    Article  CAS  Google Scholar 

  52. Dyke TR, Howard BJ, Klemperer W. Radiofrequency and microwave spectrum of the hydrogen fluoride dimer; a nonrigid molecule. J Chem Phys 56:2442

    Google Scholar 

  53. Howard BJ, Dyke TR, Klemperer W (1984) The molecular beam spectrum and the structure of the hydrogen fluoride dimer. J Chem Phys 81:5417

    Article  CAS  Google Scholar 

  54. Fellers RS, Leforestier C, Braly LB, Brown MG, Saykally RJ (1999) Spectroscopic Determination of the Water Pair Potential. Science 284:945

    Article  CAS  Google Scholar 

  55. Saykally RJ, Blake GA (1993) Molecular interactions and hydrogen bond tunneling dynamics: Some new perspectives. Science 259:1570

    Article  CAS  Google Scholar 

  56. Miller WH (1974) Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants. J Chem Phys 61:1823–1834

    Article  CAS  Google Scholar 

  57. Miller WH (1993) Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates. Acc Chem Res 26(4):174

    Article  CAS  Google Scholar 

  58. Thoss M, Miller WH, Stock G (2000) Semiclassical description of nonadiabatic quantum dynamics: Application to the S1 – S2 conical intersection in pyrazine. J Chem Phys 112:10282–10292

    Article  CAS  Google Scholar 

  59. Wang HB, Thoss M, Sorge KL, Gelabert R, Gimenez X, Miller WH (2001) Semiclassical description of quantum coherence effects and their quenching: A forward-backward initial value representation study. J Chem Phys 114:2562–2571

    Article  CAS  Google Scholar 

  60. Bowman JM, Carrington Jr. T, Meyer H-D (2008) Variational quantum approaches for computing vibrational energies of polyatomic molecules. Mol Phys 106:2145–2182

    Article  CAS  Google Scholar 

  61. Zhang JZH (1999) Theory and application of uantum molecular dynamics. World Scientific, Singapore

    Google Scholar 

  62. McCullough EA, Wyatt RE (1969) Quantum dynamics of the collinear (H,H2) reaction. J Chem Phys 51:1253

    Article  CAS  Google Scholar 

  63. McCullough EA, Wyatt RE (1971) Dynamics of the collinear (H,H2) reaction. I. Probability density and flux. J Chem Phys 54:3578

    Google Scholar 

  64. Whitehead RJ, Handy NC (1975) J Mol Spec 55:356

    Article  CAS  Google Scholar 

  65. Schatz GC, Kuppermann A (1976) Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H + H2. J Chem Phys 65:4668–4692

    Article  CAS  Google Scholar 

  66. Z, Light JC (1986) Highly excited vibrational levels of “floppy” triatomic molecules: A discrete variable representation – Distributed Gaussian approach. J Chem Phys 85:4594

    Google Scholar 

  67. Z, Light JC (1987) Accurate localized and delocalized vibrational states of HCN/HNC. J Chem Phys 86:3065

    Google Scholar 

  68. Köppel H, Cederbaum LS, Domcke W (1982) Strong nonadiabatic effects and conical intersections in molecular spectroscopy and unimolecular decay: C2H4 +. J Chem Phys 77:2014

    Article  Google Scholar 

  69. Nauts A, Wyatt RE (1983) New approach to many-state quantum dynamics: the recursive-residue-generation method. Phys Rev Lett 51:2238

    Article  CAS  Google Scholar 

  70. Sibert EL (1990) Variational and perturbative descriptions of highly vibrationally excited molecules. Int Rev Phys Chem 9:1

    Article  CAS  Google Scholar 

  71. Heller EJ. Time-dependent approach to semiclassical dynamics. J Chem Phys 62:1544

    Google Scholar 

  72. Heller EJ. Time-dependent variational approach to semiclassical dynamics. J Chem Phys 64:63

    Google Scholar 

  73. Heller EJ () Wigner phase space method: Analysis for semiclassical applications. J Chem Phys 65:1289

    Google Scholar 

  74. Leforestier C, Bisseling RH, Cerjan C, Feit MD, Friesner R, Guldenberg A, Hammerich A, Jolicard G, Karrlein W, Meyer HD, Lipkin N, Roncero O, Kosloff R (1991) A comparison of different propagation schemes for the time dependent Schrödinger equation. J Comput Phys 94:59

    Article  Google Scholar 

  75. Kosloff R (1988) Time-dependent quantum-mechanical methods for molecular dynamics. J Phys Chem 92:2087

    Article  CAS  Google Scholar 

  76. Kosloff D, Kosloff R (1983) A Fourier-method solution for the time-dependent Schrödinger equation as a tool in molecular dynamics. J Comput Phys 52:35

    Article  CAS  Google Scholar 

  77. Wang X-G, Carrington Jr T (2003) A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions. J Chem Phys 119:101

    Article  CAS  Google Scholar 

  78. Wang X-G, Carrington Jr T (2004) Contracted basis lanczos methods for computing numerically exact rovibrational levels of methane. J Chem Phys 121(7):2937–2954

    Article  CAS  Google Scholar 

  79. Tremblay JC, Carrington Jr T (2006) Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term lanczos eigensolver. J Chem Phys 125:094311

    Article  Google Scholar 

  80. Wang X, Carrington Jr T (2008) Vibrational energy levels of CH5 +. J Chem Phys 129:234102

    Article  Google Scholar 

  81. Norris LS, Ratner MA, Roitberg AE, Gerber RB (1996) Moller-plesset perturbation theory applied to vibrational problems. J Chem Phys 105:11261

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstr. 11, Haus E, 81377, München, Germany

    Sebastian Thallmair, Robert Siemering, Patrick Kölle & Regina de Vivie-Riedle

  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748, Garching, Germany

    Matthias Kling

  3. Institut für Physik und CINSaT, Universität Kassel, Heinrich-Plett-Str. 40, 34132, Kassel, Germany

    Matthias Wollenhaupt & Thomas Baumert

  4. Institut für Physik, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26129, Oldenburg, Germany

    Matthias Wollenhaupt

Authors
  1. Sebastian Thallmair
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Siemering
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patrick Kölle
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Matthias Kling
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Matthias Wollenhaupt
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Thomas Baumert
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Regina de Vivie-Riedle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Regina de Vivie-Riedle .

Editor information

Editors and Affiliations

  1. Institut Charles GERHARDT - CNRS 5253, Université Montpellier 2, Montpellier Cedex, France

    Fabien Gatti

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Thallmair, S. et al. (2014). The Interplay of Nuclear and Electron Wavepacket Motion in the Control of Molecular Processes: A Theoretical Perspective. In: Gatti, F. (eds) Molecular Quantum Dynamics. Physical Chemistry in Action. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45290-1_8

Download citation

Publish with us

Policies and ethics

Search

Navigation